$(1)$
\[
\begin{equation}
\left \{
\begin{array}{l}
T_s=200^\circ \rm{C}\\
h' = 852.39 \,\rm{kJ/kg} &
h' ' = 2792.06\,\rm{kJ/kg}\\
s' =2.33080 \,\rm{kJ/(kg \cdot K)} &
s' ' =6.43030 \,\rm{kJ/(kg \cdot K)}
\end{array}
\right.
\end{equation}\]
\[
\begin{align}
h
&=(1-x)h' + xh' ' \\
&=0.5 \times 852.39+0.5 \times 2792.06 \\
\therefore
&=1822.225 \,\rm{kJ/kg}
\end{align}
\]
$(2)$
\[
\begin{align}
s
&=(1-x)s'+ xs' '\\
&=0.5 \times 2.33080 + 0.5 \times 6.43030 \\
&=4.38055 \,\rm{ kJ/(kg \cdot K)}
\end{align}
\]